Improved Modelling of a Nonlinear Parametrically Excited System with Electromagnetic Excitation

Zaghari, Bahareh; Rustighi, Emiliano; Tehrani, Maryam Ghandchi

doi:10.3390/vibration1010012

Cited by 13 publications

(11 citation statements)

References 26 publications

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“…MCST This section studies the dynamic behavior of micro-plates under electrostatic excitation by using the modal and the Galerkin method. Among various modes that have been used, it is found that the first one is the predominant mode on the dynamic behavior of micro-plates [78]. To determine the discretized form, by applying the Galerkin method, the solution w in terms of the linear mode shapes is postulated as [79]:…”

Section: Analysis Of Dynamic Behavior Of Micro-plates In Response To mentioning

confidence: 99%

Vibration and dynamic behavior of electrostatic size-dependent micro-plates

Karimipöur

Beni

Zeighampour

2020

J Braz. Soc. Mech. Sci. Eng.

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The recent trend of using thin micro-plate structures in severe operational conditions caused the classical theory (CT) to be no longer suited in analyzing the dynamic characteristics of them. For this study, the modified version of the couple stress theory (MCST) is adopted. Then, using Hamilton's principle and Kirchhoff plate theory, the dynamic form of the size-dependent equation of motion for micro-plates stimulated by electrostatic dynamic excitation is acquired. The mixed extended Kantorovich and differential transformation methods on partial differential equations are applied to obtain the mode shapes and natural frequencies. The mode shapes from the linear free vibration solution are used as the mode shapes of the assumed multi-mode displacement field. The displacement field is required to solve the dynamical equation of motion. The equations are subsequently solved by the fourth-order Runge-Kutta method. Some universal graphs are also presented using the MCST to predict the effects of the size effect, tensile and compressive residual stresses, and aspect ratio of micro-plate on the free vibration and dynamic behaviors of micro-plates around their static configuration. It is found that the non-dimensional natural frequency parameter varies linearly versus the other non-dimensional parameters of the micro-plate. Various interesting phenomena are observed from the current simulations of the dynamic response of micro-plates to both DC and AC excitation, as well as the boundary of the frequency behavior conversion. A comparison is drawn between the responses of the micro-plate based on the modified couple stress and CT taking the size dependency into account. To facilitate understanding of the physical phenomena observed in the results, a simple physical analog to the micro-plates is suggested. This physical analog, which describes the boundary of frequency behavior conversion, is the linear relationship between the non-dimensional parameters of the system. The study of this model can help to realize some of the complex responses of the micro-plates. Keywords Vibration analysis • Modified couple stress theory • Clamped rectangular micro-plates • Extended Kantorovich method (EKM) • Modal method • Galerkin method • Differential transformation method (DTM)

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Section: Analysis Of Dynamic Behavior Of Micro-plates In Response To mentioning

confidence: 99%

Vibration and dynamic behavior of electrostatic size-dependent micro-plates

Karimipöur

Beni

Zeighampour

2020

J Braz. Soc. Mech. Sci. Eng.

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“…Once the structural model is fixed, the nonlinear identification problem is reduced to parameter estimation as only the coefficients of the model terms remain unspecified. The subject of parametric nonlinear identification is extremely broad, and an extensive literature exists (e.g., [6][7][8][9][10]). It is not intended to provide a comprehensive overview of the past and current approaches for the parametric identification of nonlinearity in this paper.…”

Section: Literature Surveymentioning

confidence: 99%

Model-Free Identification of Nonlinear Restoring Force with Modified Observation Equation

Zhang

et al. 2019

Applied Sciences

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Nonlinearity exists widely in civil engineering structures; for example, the initiation and growth of damage under dynamic loadings is a typical nonlinear process. To date, for the purpose of structural evaluation and a better understanding nonlinear characteristics of complicated structures, a number of parametric and nonparametric methods have been developed for the identification of nonlinear restoring force (NRF). However, due to the highly individualistic nature of nonlinear systems, it would be inefficient to attempt to express the structural NRF in a general parametric form. For many nonparametric techniques, their nonparametric models or approximations may result in undesirable results or oscillations around unsmooth points. In this paper, on the basis of extended Kalman filter (EKF), a model-free NRF identification approach is proposed to circumvent the limitations mentioned above. The NRF to be identified was treated as ‘unknown fictitious input’, and thus, no prior assumptions or approximations for the NRF model were required. With the aid of a projection matrix, a modified version of observation equation was obtained. Based on the principle of EKF, the recursive solution of the proposed approach was analytically derived. The NRFs provided by the nonlinear components were identified by means of least squares estimation (LSE) at each time step. Numerical examples, including building structures equipped with magnetorheological (MR) damper and shape memory alloy (SMA) damper, demonstrated that the proposed approach is capable of satisfactorily identifying NRF without knowledge or intuitive assumptions of any nonlinear model class in advance.

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“…The linear natural frequency and the linear mechanical damping ratio are measured from impact tests as ω n = 32.59 rad s −1 and ζ m = 0.001, respectively. More information regarding these measurements can be found in Zaghari (2016). Figure 3 shows the amplitude-frequency relation for step up and down tests, which are carried out by increasing and decreasing the base excitation (shaker) frequency.…”

Section: Nonlinear System With Positive Cubic Stiffnessmentioning

confidence: 99%

“…To generate a current with various phase differences with the acceleration of the shaker, a separate hardware was programmed to generate current with different phase. More details are explained in Zaghari (2016). Figure 4 shows the stable solutions versus phase φ when parametric stiffness is below the instability threshold (δ < δ th ), and when it is above the instability threshold (δ > δ th ) where δ th = 4ζ m .…”

Section: The Effects Of Parametric Stiffness For Varying Phasementioning

confidence: 99%

Phase dependent nonlinear parametrically excited systems

Zaghari

Rustighi

Tehrani

2018

Journal of Vibration and Control

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Nonlinear Parametrically Excited (NPE) systems govern the dynamics of many engineering applications, from cablestayed bridges where vibrations need to be suppressed, to energy harvesters, transducers and acoustic amplifiers where vibrations need to be amplified. This work investigates the effect of different system parameters on the dynamics of a prototype NPE system. The NPE system in this work is a cantilever beam with an electromagnetic subsystem excited at its base. This system allows cubic stiffness, parametric stiffness, cubic parametric stiffness, and the phase difference between different sources of excitation to be varied independently to achieve different dynamic behaviours. A mathematical model is also derived, which provides theoretical understanding of the effects of these parameters, and allows the analysis to be extended to other applications.

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Improved Modelling of a Nonlinear Parametrically Excited System with Electromagnetic Excitation

Cited by 13 publications

References 26 publications

Vibration and dynamic behavior of electrostatic size-dependent micro-plates

Vibration and dynamic behavior of electrostatic size-dependent micro-plates

Model-Free Identification of Nonlinear Restoring Force with Modified Observation Equation

Phase dependent nonlinear parametrically excited systems

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